Hi! I'm taking econ 2x03 (or 2g03, depending on what program you're in) with Holmes this semester, and I'm trying to prepare for the midterm next thursday. Holmes posted last year's midterms and exam for us to study with, and so far I've been understanding most of it, but I am stumped on one question:
Given the production function y=min(z1 -2, z2 -4), the efficient number of outputs when there are 20 units of z1 and 30 units of z2 available is:
A) 30 B) 26 C) 13 D) 18
According to the answer sheet, D is right. But if you need 4 of input 2 (z2), doesn't that mean the maximum you could create would be 7, since 30/4=7.5 and you need to have enough to create a WHOLE product, not just half so you round down?
Even if that was an error and there's supposed to be more of input 2, you only have 20 units of z1 so 20/2=10 units of production possible.
Sorry for the terrible run-on sentences, but I'm really confused. Can anyone explain how D) 18, is the right answer?

Hey,

You want to take the minimum value of either z1-2 (=18) or z2-4 (=26). 18 is the minimum value so D is correct.

EDIT: Forgot to add, you have enough input z1 to make 18 output and enough input z2 to make 26 output, but because this is a fixed proportions production function, you can only make as much as your smallest input allows you (sort of like the limiting reagent in chemistry). My explanation could be completely wrong since I just wrote the test yesterday with Ivanov and I am not an econ student

Wow. I just realized that I was reading it wrong the whole time. I saw Z1-2 but thought divide instead of subtract for some reason. Thanks for clearing that up for me, it relieves a lot of stress. I'll just make sure to read more carefully when I'm writing the test, lol